Black holes in general relativity coupled with nonlinear electrodynamics surrounded by perfect fluid dark matter: Thermodynamics, particle motion, and black hole shadow

This study explores black holes in general relativity (GR) coupled with nonlinear electrodynamics (NED) in the presence of perfect fluid dark matter (PFDM). We derive a singular black hole solution and investigate its thermodynamic properties, including the black hole temperature, entropy, and specific heat capacity of the black hole spacetime. The analysis of energy conditions reveals deviations from standard GR, with PFDM affecting the weak and strong energy conditions. The study further examines the impact of NED and PFDM on the innermost stable circular orbit (ISCO), demonstrating that PFDM shifts the ISCO radius and that the combined effects of NED and PFDM field parameters sufficiently influence orbital stability. Our analysis of the black hole shadow reveals that PFDM increases the shadow radius, while a higher charge reduces it, leading to modifications in potential astrophysical observables. The thermodynamic behavior of the black hole exhibits phase transitions marked by changes in heat capacity, indicating possible stability regimes. Moreover, we derive equations for black hole shadow size and study the spacetime effects on the shadow. These results provide a framework for testing alternative gravity theories and understanding the role of exotic matter in strong gravitational fields. Finally, we compare the constraints on NED and PFDM field parameters derived from our black hole model with the Event Horizon Telescope (EHT) observations of M87* and Sgr A*, providing observational limits on deviations from GR.